Question

How do you simplify `sqrt(7x)(sqrt x-7sqrt 7)`?

Answer 1

`sqrt(7) x - 49sqrt(x)`

Explanation:

First of all, expand by multiplying `sqrt(7x) * sqrt (x)` and `sqrt(7x) * 7 sqrt(7)` respectively:

`sqrt(7x) (sqrt(x) - 7 sqrt(7)) = sqrt(7x) * sqrt (x) - sqrt(7x) * 7 sqrt(7)`

... you can express `sqrt(7x)` as `sqrt(7) * sqrt(x)`...

`= sqrt(7) * color(blue)(sqrt(x) * sqrt (x)) - color(orange)(sqrt(7)) * sqrt(x) * 7 * color(orange)(sqrt(7))`

`= sqrt(7) * color(blue)((sqrt(x))^2) - color(orange)((sqrt(7))^2) * sqrt(x) * 7`

... the operations squaring and taking the square root "eliminate each other"...

`= sqrt(7) * x - 7 * sqrt(x) * 7`

`= sqrt(7) x - 49sqrt(x)`

Hope that this helped!